Documentation for fe692e8e01

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2022-01-02 02:55:05 +00:00
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<p>prints the assigned colors using <a href="https://en.wikipedia.org/wiki/Graph_coloring" target="_blank">Graph Coloring</a> algorithm
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for graph_coloring.cpp:</div>
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<tr class="memdesc:db/dc0/namespacebacktracking"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> <br /></td></tr>
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<tr class="memitem:d7/d08/namespacegraph__coloring"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d08/namespacegraph__coloring.html">graph_coloring</a></td></tr>
<tr class="memdesc:d7/d08/namespacegraph__coloring"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Graph_coloring" target="_blank">Graph Coloring</a> algorithm,. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a8c47fa37fb6eeeb781b2ec1b05af6b07"><td class="memTemplParams" colspan="2">template&lt;size_t V&gt; </td></tr>
<tr class="memitem:a8c47fa37fb6eeeb781b2ec1b05af6b07"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d3/d40/graph__coloring_8cpp.html#a8c47fa37fb6eeeb781b2ec1b05af6b07">backtracking::graph_coloring::printSolution</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt; &amp;color)</td></tr>
<tr class="memdesc:a8c47fa37fb6eeeb781b2ec1b05af6b07"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function to print the solution. <a href="../../d3/d40/graph__coloring_8cpp.html#a8c47fa37fb6eeeb781b2ec1b05af6b07">More...</a><br /></td></tr>
<tr class="separator:a8c47fa37fb6eeeb781b2ec1b05af6b07"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a976efe049deb042bf1f02612e181ab1d"><td class="memTemplParams" colspan="2">template&lt;size_t V&gt; </td></tr>
<tr class="memitem:a976efe049deb042bf1f02612e181ab1d"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d3/d40/graph__coloring_8cpp.html#a976efe049deb042bf1f02612e181ab1d">backtracking::graph_coloring::isSafe</a> (int v, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt;, V &gt; &amp;graph, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt; &amp;color, int c)</td></tr>
<tr class="memdesc:a976efe049deb042bf1f02612e181ab1d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Utility function to check if the current color assignment is safe for vertex v. <a href="../../d3/d40/graph__coloring_8cpp.html#a976efe049deb042bf1f02612e181ab1d">More...</a><br /></td></tr>
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<tr class="memitem:a40337efc5dad761096489bf2c5b1c80c"><td class="memTemplParams" colspan="2">template&lt;size_t V&gt; </td></tr>
<tr class="memitem:a40337efc5dad761096489bf2c5b1c80c"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d3/d40/graph__coloring_8cpp.html#a40337efc5dad761096489bf2c5b1c80c">backtracking::graph_coloring::graphColoring</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt;, V &gt; &amp;graph, int m, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt; color, int v)</td></tr>
<tr class="memdesc:a40337efc5dad761096489bf2c5b1c80c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Recursive utility function to solve m coloring problem. <a href="../../d3/d40/graph__coloring_8cpp.html#a40337efc5dad761096489bf2c5b1c80c">More...</a><br /></td></tr>
<tr class="separator:a40337efc5dad761096489bf2c5b1c80c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:gae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >prints the assigned colors using <a href="https://en.wikipedia.org/wiki/Graph_coloring" target="_blank">Graph Coloring</a> algorithm </p>
<p >In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AnupKumarPanwar" target="_blank">Anup Kumar Panwar</a> </dd>
<dd>
<a href="https://github.com/Panquesito7" target="_blank">David Leal</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a40337efc5dad761096489bf2c5b1c80c" name="a40337efc5dad761096489bf2c5b1c80c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a40337efc5dad761096489bf2c5b1c80c">&#9670;&nbsp;</a></span>graphColoring()</h2>
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<div class="memtemplate">
template&lt;size_t V&gt; </div>
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<td class="memname">void backtracking::graph_coloring::graphColoring </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt;, V &gt; &amp;&#160;</td>
<td class="paramname"><em>graph</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt;&#160;</td>
<td class="paramname"><em>color</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>v</em>&#160;</td>
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<td>)</td>
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<p>Recursive utility function to solve m coloring problem. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">V</td><td>number of vertices in the graph </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir"></td><td class="paramname">graph</td><td>matrix of graph nonnectivity </td></tr>
<tr><td class="paramdir"></td><td class="paramname">m</td><td>number of colors </td></tr>
<tr><td class="paramdir">[in,out]</td><td class="paramname">color</td><td>description // used in,out to notify in documentation that this parameter gets modified by the function </td></tr>
<tr><td class="paramdir"></td><td class="paramname">v</td><td>index of graph vertex to check </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> {</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// base case:</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// If all vertices are assigned a color then return true</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">if</span> (v == V) {</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> printSolution&lt;V&gt;(color);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// Consider this vertex v and try different colors</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 1; c &lt;= m; c++) {</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// Check if assignment of color c to v is fine</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span> (isSafe&lt;V&gt;(v, <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, color, c)) {</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> color[v] = c;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// recur to assign colors to rest of the vertices</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> graphColoring&lt;V&gt;(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, m, color, v + 1);</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> </div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// If assigning color c doesn&#39;t lead to a solution then remove it</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> color[v] = 0;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> }</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> }</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span>}</div>
<div class="ttc" id="anamespacegraph_html"><div class="ttname"><a href="../../df/dce/namespacegraph.html">graph</a></div><div class="ttdoc">Graph Algorithms.</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a976efe049deb042bf1f02612e181ab1d">&#9670;&nbsp;</a></span>isSafe()</h2>
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template&lt;size_t V&gt; </div>
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<td class="memname">bool backtracking::graph_coloring::isSafe </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>v</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt;, V &gt; &amp;&#160;</td>
<td class="paramname"><em>graph</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt; &amp;&#160;</td>
<td class="paramname"><em>color</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>c</em>&#160;</td>
</tr>
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<td></td>
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</div><div class="memdoc">
<p>Utility function to check if the current color assignment is safe for vertex v. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">V</td><td>number of vertices in the graph </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">v</td><td>index of graph vertex to check </td></tr>
<tr><td class="paramname">graph</td><td>matrix of graph nonnectivity </td></tr>
<tr><td class="paramname">color</td><td>vector of colors assigned to the graph nodes/vertices </td></tr>
<tr><td class="paramname">c</td><td>color value to check for the node <code>v</code> </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if the color is safe to be assigned to the node </dd>
<dd>
<code>false</code> if the color is not safe to be assigned to the node </dd></dl>
<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; V; i++) {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">if</span> (<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[v][i] &amp;&amp; c == color[i]) {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> }</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#gae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit</dd></dl>
<p>Driver Code </p>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a7">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>, and <a class="el" href="../../dd/db0/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2sorting_2wiggle_sort_8cpp-example.html#a11">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
</dl>
<div class="fragment"><div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// Create following graph and test whether it is 3 colorable</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="comment">// (3)---(2)</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// | / |</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// | / |</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// | / |</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// (0)---(1)</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">const</span> <span class="keywordtype">int</span> V = 4; <span class="comment">// number of vertices in the graph</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, V&gt;</a>, V&gt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a> = {</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({0, 1, 1, 1}), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 0, 1, 0}),</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 1, 0, 1}), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a>({1, 0, 1, 0})};</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordtype">int</span> m = 3; <span class="comment">// Number of colors</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, V&gt;</a> color{};</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> </div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> backtracking::graph_coloring::graphColoring&lt;V&gt;(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, m, color, 0);</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8c47fa37fb6eeeb781b2ec1b05af6b07">&#9670;&nbsp;</a></span>printSolution()</h2>
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template&lt;size_t V&gt; </div>
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<td class="memname">void backtracking::graph_coloring::printSolution </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, V &gt; &amp;&#160;</td>
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<p>A utility function to print the solution. </p>
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<div class="fragment"><div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> {</div>
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